The Alameda Swap Meet is a sprawling indoor market in the south of Los Angeles, where everyone speaks Spanish and you can buy almost anything. There are stalls selling Mexican food, cowboy hats, car parts, and T-shirts adorned with pictures of Jesús Malverde, the bandit who has become the patron saint of Mexico's drug smugglers.

And there's music, blasting out from the little record stores with racks and racks of CDs, album covers showing men in cowboy hats, some of them brandishing guns. It sounds like Mexican folk music, with tubas and accordions, but the lyrics are violent and explicit, praising not just the exploits of Mexican smugglers, but the murders carried out by the cartels – who in some cases have paid the musicians to write the songs.

These are narcocorridos – drug ballads – and it's a very big business, centred not in Mexico but around Los Angeles, now home to 6 million Mexican Americans and migrants. If the sales were reflected in the charts, many of these songs would be in the top 10. One stallholder says: "It outsells all other styles. It's all the young people want to buy. Narcocorridos sell a hundred times more than artists like Ricky Martin. I like the music but not the words. I don't like what they are doing to our kids."

The style itself is not new, but the lyrics reflect the increasing violence in the drug wars since an attempted crack-down in Mexico began in 2006, triggering some 40,000 deaths. While once the songs chronicled the smugglers' activities, many singers now identify with them, writing in the first person, and describe brutal killings as well as drug deals.

So Los Tucanes de Tijuana sing about narcos with "a satchel of grenades, a pistol on each leg and a bulletproof vest, dressed in black, ready for battle", El Komander brags "I like a lot of weapons and the elegant cars / Money opens a thousand doors", while BuKnas de Culiacanjoined Komander and others in the Movimiento Alterado hit Sanguinarios del M1, a praise song to Manuel Torres Félix, a leading member of the Sinaloa cartel, accused of leaving decapitated bodies and severed legs in the boot of a car. It starts with the lyrics: "With an AK47 and a bazooka behind my head / cross my path and I'll chop your head off / I'm crazy and I like to kill my enemies," while a later verse boasts "we're the best at kidnapping / We are always in a posse with bullet-proof vests, ready to execute."

Edgar Quintero, singer with the BuKnas band, said that the song had sold 100,00 copies, had 12m hits on YouTube, and gone down well with its protagonist. "Félix's daughter sent me a message on Facebook saying he liked it, so I recorded it for her live at a party and sent her the video."

Now in his mid-20s, Quintero was born in Los Angeles but sings this music "because my heart chose corridos".

But wasn't he promoting the violence in Mexico by doing this? "My dad criticises me, but it's what people my age like. It's music that fills clubs and concert halls and so I give them what they like. We're reporters – we're telling you the news."

He agrees that many of his songs are written to order, commissioned by "rich men who love spending their money and having bands playing for them, and want to hear songs about themselves". He claimed not to know if his patrons were cartel members, but then explained that the going rate is $7,000-$15,000 a song – and he is told what to include in the lyrics. This might be details of their history, smuggling successes, or their favourite guns. Quintero said he was often invited to their parties to sing in person "out of courtesy". Asked if that suggested he wasn't the most objective of reporters, he replied "Well ... I have a side job, besides being a reporter."

Quintero and his band rehearse in a garage in south-east LA. They are a cheerful seven-piece band, with an adventurous line-up that included accordion and a brass section including tuba, a vital ingredient in any narcocorrido band. Elsewhere in the US, it is fashionable to play guitar, but here, the tuba player gets the girls. The band wanted to talk about their adventurous musical policy more than their lyrics (they mix brassy banda styles with accordion-based norteno ballads) but agreed that narcocorrido was crucial for their success.

That night, at a concert in Cudahy on the ouskirts of Los Angeles, BuKnas came onstage with ski masks, fake AK47s and a genuine bazooka, purchased at a gun show. They were playing that night at the Potrero nightclub in Cudahy, which looks like a Mexican suburb of Los Angeles but is officially a city in its own right. The club was like a large warehouse covered in glittering lights, but surrounded by a large car park packed with limos and 4x4s, driven by men sporting cowboy hats and fake ammunition belts. Being "with the band" has got me into most concerts around the world, including those hosted by drug gangs in the Rio favelas, but here I was told that as an English-speaking reporter I was not welcome. It appeared that some of those in the audience didn't appreciate intruders.

The centre of the narcocorrido industry is Burbank, home to the major film studios, KBUE radio, which regularly plays the songs and Twins Enterprises, where many of them (including those of BuKnas de Culiacan) are recorded.

One of the Twins, Adolfo Valenzuela, shrugged off criticism that the songs he produces glorify violence. "It's a trend. The music has been around a long time but we've made it cool. It's what everybody wants, and whoever doesn't sing this is starving."

The industry is centred north of the border partly because there is a large market, with far more money to spend than in Mexico, and because the Mexican authorities have tried to stamp it out. Narcocorridos are banned on the radio in much of the country: this month the highly respected Los Tigres del Norte, winners of six Latin Grammys and originally known for their narcocorridos, were banned from the Mexican city of Chihuahua for daring to include just one such song, about a successful female drug-dealer, in their set.

In Los Angeles, there have been surprisingly few complaints about the songs, perhaps because Mexican Americans feel ambivalent about the music. They may not like the lyrics but they are delighted that distinctive Mexican styles have survived, and even become fashionable in the USA. And when asked why this has happened, they point to one man – the singer Chalino Sánchez, who was murdered in Mexico in 1992. He made his name in the USA partly because of his songs, including El Crimen de Culiacan, in which there are graphic descriptions of murder victims being eaten by dogs, but also because of his lifestyle. He always carried a gun, and when he was shot at by a member of the audience at a concert in Palm Springs, Sánchez immediately fired back. He was playing old-style Mexican music, but for young Mexican Americans he was now seen as a far tougher hero than any exponents of gangster rap.

Since his death, several other singers have been murdered in Mexico, starting a debate as to whether lyrics and loyalty to a particular cartel led to their deaths.

Since the attack, Ortiz's lyrics have changed, and in one new ssong Cara a la Muerte he imagines himself being killed. Valenzuela suggested that some hardcore narcocorrido singers could edge towards respectability. "The famous ones start off with this, but then they become mainstream. It's just like hip-hop and reggaeton. They use it as a bridge."

Hear more of Robin Denselow's investigation of narcocorridos in North of the Border, BBC Radio 4, 11.30am, 29 March

• This article was amended on 5 April 2012. The original referred to the Almeida Swap Meet. This has been corrected.